13.3 LOGISTIC REGRESSION AS A GENERAL LINEAR MODEL
Next, suppose we are trying to predict a binary response, such as whether or not a customer has a store credit card. In this case, the distribution of our response variable will be binary: 1 or 0, indicating a Yes or No.
The link function for a binary response variable is
![equation](https://static.packt-cdn.com/products/9781119526810/graphics/images/c13-disp-0005.png)
To isolate μ, we use the fact that eln(x) = x, and obtain
![equation](https://static.packt-cdn.com/products/9781119526810/graphics/images/c13-disp-0006.png)
The above formula ensures the mean value of the response variable, μ, will always be between zero and one. In other words, the value the regression model may be used to estimate the probability that y = 1.
To clarify that our predicted values from logistic regression are probabilities, instead of binary values, let us write the regression model as predicting p(y), the probability that y = 1. If we work backwards from our abbreviated notation, we get the parametric form of the model
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